Revista Matemática Iberoamericana

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Volume 35, Issue 6, 2019, pp. 1745–1762
DOI: 10.4171/rmi/1100

Published online: 2019-08-20

On bodies in $\mathbb R^5$ with directly congruent projections or sections

M. Angeles Alfonseca[1], Michelle Cordier[2] and Dmitry Ryabogin[3]

(1) North Dakota State University, Fargo, USA
(2) Chatham University, Pittsburgh, USA
(3) Kent State University, USA

Let $K$ and $L$ be two convex bodies in $\mathbb R^5$ with countably many diameters, such that their projections onto all 4 dimensional subspaces containing one fixed diameter are directly congruent. We show that if these projections have no rotational symmetries, and the projections of $K,L$ on certain 3 dimensional subspaces have no symmetries, then $K=\pm L$ up to a translation. We also prove the corresponding result for sections of star bodies.

Keywords: Projections and sections of convex bodies

Alfonseca M. Angeles, Cordier Michelle, Ryabogin Dmitry: On bodies in $\mathbb R^5$ with directly congruent projections or sections. Rev. Mat. Iberoam. 35 (2019), 1745-1762. doi: 10.4171/rmi/1100